This is the first time I ask a question on Mathoverflow, so I apologize in advance if it is not suitable/a duplicate/otherwise inappropriated.

I am thinking about Voevodsky's category of motives and I realized that in his presheaves with transfers formalism pullbacks for Chow groups are defined for arbitrary maps of smooth schemes. Precisely if $f:X\to Y$ is a map of smooth schemes and $\alpha\in CH_*(Y)$ he defines

$$f^*\alpha = (pr_1)_*(\Gamma_f \cdot (pr_2)^*\alpha)$$

where $pr_1,pr_2$ are the projection maps from $X\times Y$ and $\Gamma_f$ is the closed subscheme of $X\times Y$ determined by the graph of $f$ (note that $(pr_1)_*$ is well defined more or less because the restriction of $pr_1$ to $\Gamma_f$ is an isomorphism).

After researching a bit I found a paper by Bloch ("Algebraic cycles and Higher K-theory") he seems to define the pullback for all maps with smooth target. However in classical treatments of intersection theory I've only seen $f^*$ defined for flat maps.

**Q:** In what generality is the pullback of cycle classes defined?